摘要
基于已发展的二阶微商三次样条四阶逼近公式，提出了数值求解含源汇项扩散方程的二层三点且在空间方向上达到四阶精度的加权差分格式．通过Ｆｏｕｒｉｅｒ方法讨论了文中格式的稳定性．证明了当１／２θ１时，格式是无条件稳定的，而当０θ＜１／２时，只有０＜ｒ１／［３（１－２θ）］，格式是稳定的．其中θ是权参量，ｒ＝Ｄτ／ｈ２为Ｆｏｕｒｉｅｒ数，Ｄ为扩散系数，而τ。
A class of new weighted difference schemes with higher accuracy is proposed for solving one dimensional diffusion equations. The method is based on the cubic spline difference formula of fourth order accuracy for second order derivatives developed by the author, with a truncation error of order O[(2θ-1)τ,τ 2,h 4] , where τ and h represent the time and space steps respectively. The present method is unconditionally stable if 1/2θ1. However, when 0θ1/2 the method is stable only if 0<r1/, where θ is the weighting factors and r=Dτ/h 2. The results prove that our method is highly accurate.
基金
国家自然科学基金
关键词
扩散方程
加权差分格式
稳定性
精度
有限差分法
diffusion equation, weighed difference scheme, numerical stability, high accuracy, computational fluid dymamics
